Similar masses gravitating stably together

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The discussion centers on determining the maximum number N of equivalent masses M that can stably gravitate together within a radius R. Participants clarify whether "mutually gravitate" refers to maintaining stable circular orbits around a common center of mass. The N-body problem is referenced, highlighting that for N greater than 2, the masses can have non-circular orbits but still remain confined to a distance R from the center of mass. The conversation seeks to establish the minimum limit R(N) for N equal masses to co-orbit perpetually. Overall, the focus is on the dynamics of multiple gravitating bodies and their stable configurations.
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What is the greatest number N of equivalent masses M which can mutually gravitate over time within a radius R?
 
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"Mutually gravitate over time with radius R"? Do you mean stably move in a circular orbit (about their common center of mass) with radius R?
 
HallsofIvy said:
"Mutually gravitate over time with radius R"? Do you mean stably move in a circular orbit (about their common center of mass) with radius R?

As an example, consider the N-body problem where N>2, M=M0=constant, and R is a function of N (and possibly M0). The orbits are not circular, but might be confined "stably" to a distance R from the center of mass.

N>2 equal masses co-orbit perpetually within what minimum limit R(N)?
 

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